Classically, optimal control research has focused on the study of methods for trajectory optimization of underactuated nonlinear systems.
This attention is due to the fact that underactuated systems are more difficult to control due to having more degrees of freedom relative to the number of controls available [1]}.
However, the emerging UAM sector allows the opportunity to study the application of optimal control methods to overactuated aircraft whose complexity appears in the nonlinear transition dynamics between flight phases [2]}, [3]}.
These UAM class vehicles commonly exhibit three phases of flight — including VTOL, fixed-wing cruise, and a complex transition phase between the two — and can thus be classified as hybrid systems [4]}, [5]}, [6]}, transitioning between multiple modes of the dynamics during a flight.
While many algorithms have been developed for hybrid systems trajectory optimization in the past, most adopt a linear or reduced-order model, with the focus on bipedal or quadrupedal robotics systems, e.g. [7]}, [8]}, [9]}.
The lack of applications to UAM class vehicles reveals an opportunity to develop hybrid systems optimization techniques for unique aircraft dynamics which have not been previously studied.
